Block #1,216,919

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/1/2015, 9:54:17 AM · Difficulty 10.7240 · 5,627,583 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

65ac7decfd005c46dbd36bf00af8b2fda0223124c3d4448bd2c6e9639e7fc34d

View on Chainz ↗

Height

#1,216,919

Difficulty

10.723953

Transactions

Size

885 B

Version

Bits

0ab95502

Nonce

1,246,787,604

Timestamp

9/1/2015, 9:54:17 AM

Confirmations

5,627,583

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

9164eebf9af42656249f8a2f40fc8f76aae18c54deedcd5bd04bc6ca7e844c34

Transactions (4)

Coinbase8af086a75313b1…dda0de687fa3b0

1 in → 1 out8.7100 XPM116 B

AJCEY9yy…tg97E6zm

80765769c62d9d…4e4dd351718287

1 in → 2 out5.9203 XPM227 B

AMHK5Hy6…fiBMiLxK ARCWcRwi…jDL84RrD

406b0412746a4f…8465a21f41c930

1 in → 2 out3.9720 XPM225 B

AJZLosn4…vGxWSs1k AcuM7XiJ…5uND8Jce

8609a7830ce539…b54376a2474cd8

1 in → 2 out6.5354 XPM226 B

AXWveKZz…t4DZJK4K AeukXgki…QeSgEWVD

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.032 × 10⁹⁶(97-digit number)

20329601034949560985…70424968771571783679

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.032 × 10⁹⁶(97-digit number)

20329601034949560985…70424968771571783679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.032 × 10⁹⁶(97-digit number)

20329601034949560985…70424968771571783681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.065 × 10⁹⁶(97-digit number)

40659202069899121970…40849937543143567359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.065 × 10⁹⁶(97-digit number)

40659202069899121970…40849937543143567361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.131 × 10⁹⁶(97-digit number)

81318404139798243941…81699875086287134719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.131 × 10⁹⁶(97-digit number)

81318404139798243941…81699875086287134721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.626 × 10⁹⁷(98-digit number)

16263680827959648788…63399750172574269439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.626 × 10⁹⁷(98-digit number)

16263680827959648788…63399750172574269441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.252 × 10⁹⁷(98-digit number)

32527361655919297576…26799500345148538879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.252 × 10⁹⁷(98-digit number)

32527361655919297576…26799500345148538881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,216,919

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